JP2006-8009 A discloses a parking assist apparatus used for a vehicle in which only front wheels can be steered, wherein a traveling path for guiding a vehicle to a target position is calculated using a rear axle center of the vehicle as a reference point. The calculated traveling path includes a section in which the reference point creates a trajectory of a clothoid curve. Further, in JP2006-8009 A, the following is described; in the case of the vehicle having a four-wheel steering mechanism, it is possible to implement the traveling of the vehicle along a target travel trajectory by steering rear wheels, while performing steering control according to a steering control pattern.
In the case of a vehicle (referred to as a 2WS vehicle, hereafter) in which only front wheels can be steered, a turning center is always located on an extended line of a rear wheel axle of the vehicle. Thus, when a turning curvature of the vehicle is increased in proportion to an amount of movement of the vehicle, an axle center of the rear wheels (i.e., a rear axle center) of the vehicle creates a trajectory of a clothoid curve. Therefore, if the traveling path is calculated using the axle center of the rear wheels as a reference point as disclosed in JP2006-256356 A, there are advantages in that the path can be calculated easily using the clothoid curve and thus the calculation workload or the like can be reduced.
However, in the case of a vehicle having a four-wheel steering mechanism (referred to as a 4WS vehicle, hereafter), that is to say, in the case of a vehicle which has a four-wheel steering mode in which the front wheels and the rear wheels can be steered independently, when the front wheels and the rear wheels are steered simultaneously, the turning center moves in a forward direction of the vehicle and thus the trajectory of the rear axle center of the vehicle no longer becomes a clothoid curve. Further, in the case of the 4WS vehicle, when the front wheels and the rear wheels are steered simultaneously, the turning center moves in a back-and-forth direction as well as a lateral direction of the vehicle, depending on a relationship between steering angles of the front wheels and the rear wheels, which makes the generation of the traveling path difficult.